Sometimes people say that water is removed from clothes in a spin dryer by cen88ibg2:rr-cif csv b /zzup;, trifugal force throwing the water outward. What is wrong with this st;g 8b2rz,uip fz8b/scc-irv:atement?

Will the acceleration of a cavp(4xt wd-hs;r be the same when the car travels around a sharp curve at a constan4thp( ;w-xvs dt 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly rola8f-sbc); d oad. Where does the car exert )8asc-;d fblo the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-go-r83qwnpls6hj5qc3v01q a wbd *ound. Which of these foavpbswq 6 n1l8w5q j *3cdq30hrces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without t , vel*kewz9(ar;nj37, zxnwyhe water spilling out, ek 3we;z*e7a,xj,wrny 9l(vnz ven at the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at l6d byfw1- kg5ieast three controls in the car which can be used to cause the cark-d 1wiy5 b6fg to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest obja) kzwo2u+:2ax bhs3d.l k ,f a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.ds: z.xh2 uwbob+),3kj2l aak

Why do bicycle riders lean inward when rounding a curve at hig mo: f:sa f8jqh-vo;nzd -/w:gh speed?

Why do airplanes bank when*)1a2scy 5rcdsol 7bj they turn? How would you compute the banking angle given its speed and radius of the turn?b ) ss 5ard*jclo2cy71

A girl is whirling a ball on a string ay /mu 43tzc)xfu::kca round her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let tf4ua 3y)muc:x :ck/z go of the string?

Does an apple exert a gravitatioxv/s-i2dx .i:it1w 3 xh l2lodnal force on the Earth? If so, how large a force? Conside xwls:vi/i12xio. h- 3 xltdd2r an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in whal-s2xwl7v) zqhsnh9 8t ways would the Moon’s orbit be di2h9vnwl-z87 h)sxql sfferent?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon on the -l7llvk:uu/ ; uqur7lEarth? W uku l vl;l77:uul/-rqhich accelerates more?

The Sun's gravitational pull on the Earth isplr-l h i*9;xf much larger than the Moon's. Yet the Moon's is mainly responsible for the tidesxl-fh9* l rip;. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at t*3m, wapxnht5a.7 )tvbmx/mvb n.b)h+0cyk zhe equator or at the poles? What two effects are attw a)bm n p xahmbxt+/,0cby7*n5.vhv.)3km z work? Do they oppose each other?

The gravitational force ;lo . 4cw6z rbdu+pm0ion the Moon due to the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away from i0 r;.uwpzb lc64+odmthe Earth?

Is the centripetal acceleration of a,),fj(bdc k0pa 7fukcp6q(a7j:tno Mars in its orbit around the Sun larger or smal7nuocab ad)qff76 ,,0pajk((j:pt kcler than the centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east or oqw/ ; e ah3+ef 6)thimyymjo7(n4qj+ (b) toward the west? Conm+ja3( eih7 y/qhtqoj ;m6y)w+f eno 4sider the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by a scale in a f(t (on;g j1b zz9)bxk ,jo+eb0mssv7moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you nojv0(g9s+zo t;) xbe1s7,bmb k fz j(are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periodsd v6 ex)pobwez:( g3)o in outer space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). E )wvo xbzd:)6g(3e eopxplain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “a0l( :: r t3qlj *pmooz+kzfm/qpparent weightlessness” between st3:* ljp m0(otz/k :r qfzl+omqeps.

The Earth moves faster in( z s;3zkmd*xz+hmu+l its orbit around the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s msmz d*u3;lxz++z(k haxis relative to the plane of its orbit.]

The mass of Pluto was not known untiu/o*+pukv , :3ccx ezxl it was discovered to have a moon. Explain how this discovery enabled xp*3,ecuuco:zxk+/v an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's. Yet th(q *bs5 opp g2ft)xb/ve Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to t /o2pvqx b5 )*spfg(bthe other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane travelin :ylg*x+xjc8m8vu6bb n+ rr;hg 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in iju j td)n:6pug hf6e 1myuh31yz 0yq6*ts orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Asmhn3t1 :hu 0*pgu6yj 6 1u)qzjeyf 6dysume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exei.ln 8/2puqe vnku0tb 58ky1krted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of k8e yu8kitp/ql vnk.n50b 2u1 radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space sh.1v m;go,5kxw p8.2ucoaaa qa uttle is in orbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , ag;2auvp5o.xcaqo wma ,1. k8the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay,hhd y1jm.c j7 7tay+l on the edge of a potter’s wheel turning at 45 rpm (revolutions per mi1y+jc l my7d.haj 7th,nute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved atriw-;t -;0 m s+gi;y0dojwsrj a uniform rate in a vertical circle oftm s; ywijwj0gri+ --d;sr o;0 radius 72.0 cm , as shown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

  A 0.45$-\mathrm{kg}$ ball, attached to the end of a horizontal cord, is rotated in a circle of radius 1.3 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75 N , what is the maximum speed the ball can have?   

  What is the maximum speed with which a 1050-kg car uf2x), y+ib,8 jhwq pjcan round a turn of radius 77 m on a flat road if the coefficient of static friction betwee i ,hw2jjxy8,f)+ pqubn tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static frictiomb5dj:;w ,g.cu y nb bh037vfen be between the tires and the rb wmvy bj b3n.;c ugfed05h7:,oad if a car is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jemks;7wxig14(hn8lr spz9gy fu*to1+g lpd2.t fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is;xk.f+ld9h18s4 n *pr7iowu2tl1zg y(m gs gp 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axouifp0 z4 q-* z.nm+tkis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm u.n+kzi0fmp q4zto -* is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upsidehgecw zql,p 89t:+; jzka x53e down at theg:;39qph5,aztx w8e+ej kl zc top of a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosses the roundefif4m1 h5vj5 atnu)v h( lq,4nd top of a hill vf1jvh45q,h n u(a lft )i4m5n(radius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Ferrispfpkesj1*/w/d d oiy 8p1:cb0 wheel need to make for the passengers to feel “weightlejec:fp1*k/ d io8p/1wy pdbs0ss” at the topmost point?    rpm

  A bucket of mass 2.00 kg i ur2)q0rzafw ,s whirled in a vertical circle of radius 1.10 m. At the lowest poin ruqar20z,wf) t of its motion the tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a particle 9.00 cm f:f7b21in 6ryj ;9lqbszrf x 6arom the axis of rotation is to experience an accelerab ;f6fl6yiq2r:z9xr jna7bs1tion of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically walle/(rw/kt 0 vkogd "roo0gk w/rv /(ktom." (See Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle oeerrj 1zneb84 u.hr9 a eh* jx0ni3;,fn a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a cent9zejbr1, i.8*hrn0e;3eu naf xr4 ejhral hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

$v=\sqrt{\frac{m g R}{M}}$

  Redo Example 5-3 , precisqupb:a:r+ft/c9zzt9/ dl ko :ely this time, by not ignoring the weight of the ball which revolves on a string 0.600 m lo/pr9b f:d/ z az tql9kco:t+:ung. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked for a cdn2.yk bp;alaugs.tw76sq+- ar traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

  A 1200$-\mathrm{kg}$ car rounds a curve of radius 67 m banked at an angle of 12$^{\circ}$ . If the car is traveling at 95$ \mathrm{~km} / \mathrm{h}$ , will a friction force be required? If so, how much and in what direction? $\approx$    down the plane

Two blocks, of masses h)ws:5u*;idked/iv z $ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an evasive maneuver by diving vertically at 310v*6t ewe/rk( l i/w(yx23kxpm $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centr( alvcf.i 8eq+e4+zxx*qmps sz8 x i66ipetal components of the net force exerted on the car (by the ground) in Exa.+ec 4ie p+l8m86axz6xsqfs z *i(xvqmple 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from the pit area, goigaw;t np 4,q) :gt:jwjng from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceler,tgn4tjjw :wqg a) :;pation. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . Atv)sy f66un c/8akpz7d a particular instant, its acceleratiy)kzf av 66up7ncds8/on is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a r) *dpebhkgz)h7:10 y3 wjfmm spacecraft 12,800 km (2 Earth radii) above t 7b3)em0p)j f1zhm gy* rhdkw:he Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g has a ma7b+lcs- q3l 6taq3s kwgnitu6sl+3 wba 3lt7qqk-scde of 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravitc6vs*w5 5noohx0 mot1x+ ong+y on the Moon. The Moon's radius is 1.74 ho0 onosc5+wn 6tmxv5+1*oxg$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 jm yf:p4 e9k-2q3ggmq times that of Earth, but has the same mass. What is the acceleration due to43kqj9eq-fm : ypmgg 2 gravity near its surface?   

  A hypothetical planet has a mass 1.66 times thatq(;lq ,zzlkx3hn q73o of Earth, but the same radius. What is g near it qz ql,37 klq(3hx;ozns surface?   

  Two objects attract each other gravitationally with a force of cjnp+2y n5v n,2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of9 (oat1,icuyy10pb mkyw-y y q0-4.q pl1afi c g , the acceleration of gravity, at (a) 3200 m i9k -p14 y(a.yp10btlo0 qyaif-,yqwmc yuc 1   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth whe*n*ea4g,gc3g0s m zacre thez n *geg,sg* m430accagravitational acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times lomd:dluz62 .the mass of our Sun packed into a sphere about 10 km in radlmdlz6: od. u2ius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average stn*xu wa9vz2) yar like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface grawaynzx 9*)2vu vity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbi rv/h)- kqr hdr- p2qhj8 ,any*f9+lubting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acnpq/r b9f lk2q r-h+drh 8,vua*-j)yhceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at thous0:g;yp h5he2n xljr0aa5 /e corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by t:ae5h lh0prj y0n/ogx 52sau;he other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same side of t +4y9ro6z zgkkuo.r1a he Sun. Calculate the total force on the Earth due toayz+4gzo 9.krk u o1r6 Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface of Mars is 0.38 of y-fa + -g9ap,3hlgawf what it is on Earth, and that Mars’ radius is 3af9hwal- p 3a, yf-+gg400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of the Earth2n ydps) s3p9tfn+g -s 3j,nxv and its distancvx-)n np s fgt9nsy p,j+s332de from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit abdvvih w5i- bot:of625bb,9 ubout the Earth at a height 5:d9i o5ufbv -,wtb2ovi bh6b of 3600 km.    $\times 10^3$

  The space shuttle rel6k0o.sl iw3zk eases a satellite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to 3l 0szo6k k.iwEarth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if och g uk ja)u5ubgf4g( 8:-cciv;cupants are to experience simulated grau:84h)cgvgf(uj;u k5gb a- ci vity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a circular “dkpstu3mt eql5 : .7 *vpvh04qnear-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compav*dp5hpt.4lv3te 0s7kmq uq:red to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched from the to3 k.sopn3xon8c 6 q.v1 (fcgoip of Mt. Everest to be placed in a circular orbit around the Earvo 6.i 38fc3n1 oxsc po(qkg.nth?   

  During an Apollo lunar lah3 : zivd80uranding mission, the command module continued to orbit the Moon at an altitude of about 100 km. How long did it taud:8ivahr 0z3 ke to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the plane4pj li h0,a8crt. The inner radius of the a0l rj4pi,c 8hrings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


$T_{\text {irner }} $ =   
$T_{\text {outer }} $ =   

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s (see Fig. ;q 5el7ic2hup 0k +5hgr7 e libj2;ppg5–9). What is the ratio of a person’s apparent weight to her re qj0luhhg2p e77+plg2;ki 5i;r becp5 al weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the center5nnolyk / f5, xj rmo3+3k3rit of the Earth's Moon in a space vehicle (a) moving at constao + /n3lt35fjx3n riro,mkk5y nt velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars of equal mafyo (9l j2h*gch g8zaq8 vk..uss. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between t9.hqkj*8c2uvy (zh8 o lag.gf hem. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for l-,ntf.z5qaa: 4salmt;g 4uwthe weight of a 55-kg woman in an elevator that m;q- f:4gnttlsa5z.au,wlm a4 oves
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from the ceiling of)iqamahy9 wv- -s c,ae-3 pza+ an elevator. The cord can withstand a tension of 220,s3awa)zcv--ih a9qpy a-+me N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet with period T t-e6n oz :idrlig) j*8vqs:m8x di4*n , the density (mass/volume) of the planet is 8ti:d) n:i4 lmzg i*ore-6sn8djv qx* $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (+dkgdh p+jd15 wo y*u9 fj,)zt27.4 d) to determine the period of an artificial satellite orbiting very near the Earth’s surfa1 5ot*kd+)fu wgyj+,9djzph dce.    s

  The asteroid Icarus, though only a few hunado:r)il.b9e dred meters across, orbits the Sun like the planets. Its period i )doib9 :.lears 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4.5 1 x 4klf-+tq:yfo6esakdf/7u $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every ,0fjoxqycbiy5sdz t ).a8 l;;76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and;5,ox) y qt8dslfyica.bj;0z farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of thymfc1o/ano3y,u k (a -e Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, e nfy( i;qd xeikif (:s:b:q80and mean distance for the four largest moons of Jupiter (those discd:n:kqqibsife8(0;e fx y:(i overed by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period and dke5ghx: +mh)p 9kb vw8istance of the Moon. m9 he8vbg+hk )xp 5w:k   $\times 10^{24}$

  Determine the mean distance from Jupid* m8l 7(muvmlter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods giv m8 *dlul(mm7ven in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars an5ya nn.rn7 *zs4jxf 6ld Jupiter consists of many fragments (which some space scientists think came from a planet that once orbited the Sun but w rlf5j 6*nx.7 znyas4nas destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "pas*67n, 3gu0agkkir elanet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent g *0,7arukksi ag6neg3ravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gori55,d eogk6kx ge by swinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting6 5kdxeg5o ,ki a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the accelerbz29x,anmh fzr*.tf+ ation of gravity be half what it is on the h xm+b rzft92,n zaf.*surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab handq9np5bd(wx4. krdo:zs and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.:w noxkb4(r9.dd5pz q80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates ,:+d,ueuguz8d gh7qu once per day, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction oq7u 8,e+dhggu z,:uudf g is this?    $\times 10^{-1}$

  At what distance from xzujc m)n ,f8hnz2f+s8l4t6soqn3 ( bthe Earth will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earts us lnzqmx+ ,(f84 z8) nfc62bohntj3h and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a va (nma8k/a :lm;si/ tbathroom scale in an elevator, it says your mass is 82 kg. What is thka8(n/il;m /vaam t:s e acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a cie:pz1+yit6r yrcular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutionspezt:i6ryy1+ per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft incowxg9l--p q:ob9od 6 a vertical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of its ra9 2s ew r/apl(o7:t xpsawz)h7dius r, the acceleratiow:o9lr a7 ppszesa7th/w)(x 2n due to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the ve gvy 0djc1w0;jrtical by an angc j0j0y 1;dvwgle $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is- jx7cvl3-gmm banked for a design speed of If the coefficient of static friction is 0.30 (wet pavementmgmc- 7xl-3jv ), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth8 9lp,8 elkggs:zj eg- were rotating so fast that objects at the equator were apparently weightles l9pgjel:8sz 8egk ,-gs?    $\times 10^3$s

  Two equal-mass stars mainthne-vekqh2vvg-x*6x5 l *u3tain a constant distance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a cur0u e9guu mgd-u73q; vhuahwnl/8i.6fve of radius 235 m. A lamp suspended from the ceiling swings out to an ann3u6 hegwlq-ga7u vui uu f0m.dh;8/9 gle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as tiub5m ,60h)zz hyg,.mc:xeut ; zq-ubhe Earth. Thus, it has been claimed that a person would be crushed by thb).ibh :cu ,,hxmem 6tz-;zuy 5uqg0ze force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced7rc;twc+ o3mi+x9wd o 8otpp/ the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a blo+o w/d+ rmxowtt793 ppi8;ccack hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill andn wqt *tx .ld 7rfbf/h0i+-.pu valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Wherw0uf pn.qbr/i*txdf7h.-tl+ e would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 satelll;0iqers :n /8j3u zdeites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distribu q erze;juls/i d80n:3ted evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR),(emjq nl/n5sfq9 rv: ahx2u lj974od- after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km .qu42romj5f :a(nj-9l 7edsnlhvq / 9x Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a sate k.-nu c7t.ptv. h7l +omhee(pllite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km be.7p7ok.lutthn v.(emche-p+ hind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) Wham4 *06wl,;4yre6mmlnkki4xikp p: qvt is its mean distance from ripmqxemkil 44,k:*wy l0 v ;6kmp 4n6the Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you could actuallg,e av,w(+dk 0g -srt2in6z idy "feel" yourself gravitatd6,a0n , 2-dve (iwir gt+gkszionally attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around ththy b9q ud/6l/e center of the Milky Way Galaxy (Fig. 5-46) at a distance of a6hylu/ 9qbd/ tbout 30,000 light-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.50 m on eaccwts8 6z0a)uu; t.b7yo eo9fih side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass p7zf t )uywsao 8utic.ebo0 96;laced at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 550 or -ko.i ogzxal7a(dkk09b9x h.,tn50 kg orbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1/qlwtsk - 28(kv*u emz.5-cm-long sweep second hand on your wrist watch?-k82*qtl usvzwk e m(/    $\times 10^{-4}$

  While fishing, you get bs5 rvjr(9vd m1ored and start to swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle sv 5m (j1v9rrdevery 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R iu dvd4ukf, ;3z3je+9h j1u wtwn a new highway is designed so that a car traveling at spdv 931 e+wfjuu,j ;d43t wuhkzeed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, thp.bg:6i :(c ilav- bzbe Acela, utilizes tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengzbbb(il:-gip va.c 6:ers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train does not tilt. $\approx$    $\times 10^2$
(b) Calculate the friction force on the passenger if the train tilts to its maximum tilt of 8.0º toward the center of the curve.$\approx$    $\times 10^2$